The project develops models for analysis of multiple event times. Two projects are considered in this proposal. The first project proposes new methods for regression analysis of a class of stochastic process models called modulated renewal processes. They can be used to model multiple event times representing specific episodes in the disease progression of a patient. In this project we propose extensions of accelerated failure time and transformation models. We also consider parameter estimation in these models. The second project considers matched pair competing risk regression models. Models of this kind arise in biomedical and actuarial follow-up studies. In such studies, matching (or blocking) serves as a method to control for effects of prognostic variables on the variability of the outcomes represented by time and failure type. We propose a class of stochastic process models for analysis of matched pair competing risks. Both projects develop also applications to analysis of follow-up data from bone marrow and kidney transplant studies. We consider prediction of patient post-transplant experience based on pre-transplant characteristics and follow-up history.